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研究生:謝詮
研究生(外文):Chuan Hsieh
論文名稱(外文):On the Blow-up solutions of Biharmonic Equation on a ball
指導教授:陳建隆陳建隆引用關係
學位類別:碩士
校院名稱:國立中央大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:19
外文關鍵詞:blow-up
相關次數:
  • 被引用被引用:0
  • 點閱點閱:131
  • 評分評分:
  • 下載下載:3
  • 收藏至我的研究室書目清單書目收藏:0
在這篇論文中我們主要探討Biharmonic Equation and
Polyharmonic Equation 在有限區間解的行為就能Blow-up 。
在第一章節中我們以介紹的方式瞭解現今數學家對此方程式中
的探討跟瞭解並且給予正確的定義和主要定理的敘述,在第二章節裡
我給予Lemmas 做先前的預備知識,在第三章節中我給予定理完整的
證明,而在最後一個章節中列出相關文獻提供各位讀者參考。
In he paper we are consider for Biharmonic Equations and Polyharmonic Equation in the finite interval will Blow-up.
In the chapter 1 we are introduce the main theorem and to definition equation.
In the chapter we give some Lemmas in order to proofs theorems 1.1 and 1.2
In the chapter 3 we proofs of theorem 1.1 and 1.2,and the last chapter we give the references
CONTENTS
1. INTRODUCTION……………………………………………2~5
2. PRELIMINARIES……………………………………………5~13
3. MAIN THEOREM……………………………………………13~18
REFERENCE……………………………………………………………18~19
References
[1]Sattinger, D.H.:Conformal metric in R2 with prescribed carvature. Indi-
ana Univ. Math. J. 22, 1-4 (1972).
[2]Oleinik, O.A.:On the equantion 4u+K(x)eu = 0. Russian Math. Surveys
33, 243-244 (1978).
[3]W-M.Ni, On the elliptic equation 4u + K(x)e2u = 0 and conformal met-
rics with prescried Gaussian, Invent, Math. 66 (1982), 343-352.
[4]T.Kusano and S. Oharu, Bounded entire solutions of second order semi-
linear elliptic equation with application to a parabolic intial value problem,
Indiana Univ. Math. J. 34 (1985) 85-95.
[5]W-M.Ni, On the elliptic equation 4u+K(x)u
n¡2
n+2 = 0, its generalizations,
and applications in geometry, Indiana Univ. Math. J. 31 (1982), 493-529.
[6]R.McOwen,On the equation 4u + K(x)e2u = f and prescribed negative
carvature in R2, J. Math. Anal.Appl. 103 (1984), 365-370.
[7]Kazdan, J., Prescribing the curvature of a Riemannian manifold, NSF-
CBMS Regional Conference Lecture Notes 57 (1985).
[8]Cheng, K.-S. and Lin, J.-T., on the elliptic Equation 4u = K(x)u¾ AND
4u = K(x)e2u;Trans. of the Amer. Math.
[9]Cheng,K.-S. and Smoller, Joel A.,Conformal metrics with prescribed Gaus-
sian curvature on R2,Trans.Math.Soc. 336 (1993), no.1,219-251.
[10]Lin, C.-S., A classi‾cation of solution of a conformally invariant fourth
order equation in Rn, Comment. Helv. 73(1998) 206-231
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